Under the Olive Trees: A Multimarket Liquidity Demand Model for Derivatives-Implied Arbitrage Spreads

Abstract

We study the connection between liquidity demand and derivatives-implied arbitrage spreads. We develop a novel spillover hypothesis, which conjectures that for an arbitrary number of derivatives markets that share common financial intermediaries and the same underlying spot market, there exist intermarket spillover effects in which leverage demand in one derivatives market impacts derivatives-implied arbitrage spreads in multiple derivatives markets. We formulate a multimarket liquidity demand model in which dynamic interactions between financial intermediaries and end-users across futures, options, and spot markets influence asset pricing in these markets. We use our model to make three predictions about the relationship between U.S. equity index futures liquidity demand and U.S. equity index options-implied arbitrage spreads. 1) Changes in the options-implied arbitrage spread have a contemporaneous negative relationship with changes in futures dealer demand and a contemporaneous positive relationship with changes in futures end-user demand. 2) Changes in the options-implied arbitrage spread have a contemporaneous positive relationship with both futures returns and spot returns. 3) The options-implied arbitrage spread has a predictive negative relationship with both futures returns and spot returns. We then test our model's predictions through a series of regression analyses - regressing changes in the options-implied arbitrage spread on changes in futures investor net positioning, regressing contemporaneous market returns on changes in the options-implied arbitrage spread, and regressing future market returns on the options-implied arbitrage spread. We find evidence in the data in support of both our liquidity demand model's proposed explanation for derivatives-implied arbitrage spreads and our spillover hypothesis. By recasting our options-implied arbitrage spreads as options-implied Treasury convenience yields, we additionally elucidate the extent to which changes in leverage demand underlie fluctuations in the convenience yield.